In the detector system in accordance with U.S. Pat. No. 6,027,627, fluoresced light from migrating species within a plurality of capillaries aligned in parallel passes through a filter, a transmission grating beam splitter and a lens before it impinges on a CCD detector array. In the preferred embodiment, the CCD detector array comprises 1024×256 pixels. The first dimension, (1024 pixels) covers 96 parallel capillaries, each capillary being focused onto at least one of the 1024 rows, although the number of rows per capillary can be increased by selecting a lens with a different focal length or changing other optical parameters. The second dimension (256 pixels) covers the fluorescence spectrum spread by the transmission grating.
In this prior art system, both the first order and second order components can be focused onto the detector array, although this is not an absolute requirement. What is required, however, is that a spectrum (such as represented by the 1st order components) be created for each capillary and detected. The spectrum of interest should include the wavelengths of light at which the dyes are known to fluoresce. The spectrum of interest for each capillary is spread over P contiguous pixels and these are divided into R channels of Q contiguous pixels, R=P/Q. R should be at least as large as the number of dyes M being used and preferably is greater than this number.
The detector of the prior art system outputs a spectrum comprising R light intensity values for each capillary, each time that data is provided to the associated processor. The processor then maps the spectrum of R intensity values for each capillary, onto values which help determine which dye has been detected in that capillary. This is typically done by multiplying calibration coefficients by the vector of intensity values, for each capillary.
The principle behind the calibration coefficients is that a spectrum of received light intensities in each of the channels is caused by the spectrum of a single dye (tagging a corresponding base) weighted by the effects (calibration coefficients) of the detection system. If I0(n), I1(n), . . . , I9(n) represent the measured intensities of the R=10 channels at the nth set of outputs from the CCD (after preprocessing including detection, binning and baseline subtraction), B0(n), B1(n), . . . , B3(n) is a vector representing the contribution (presence 1 or absence 0) from of the M=4 bases, and Cij are coefficients of a known 10×4 matrix which maps the bases onto the detected channels, we then having the following relationship:
                              (                                                                                          I                    0                                    ⁡                                      (                    n                    )                                                                                                                                            I                    1                                    ⁡                                      (                    n                    )                                                                                                                                            I                    2                                    ⁡                                      (                    n                    )                                                                                                      …                                                                    …                                                                                                          I                    9                                    ⁡                                      (                    n                    )                                                                                )                =                              (                                                                                C                    00                                                                                        C                    01                                                                                        C                    02                                                                                        C                    03                                                                                                                    C                    10                                                                                        C                    11                                                                                        C                    12                                                                                        C                    13                                                                                                                    C                    20                                                                                        C                    21                                                                                        C                    22                                                                                        C                    23                                                                                                …                                                  …                                                  …                                                  …                                                                              …                                                  …                                                  …                                                  …                                                                                                  C                    90                                                                                        C                    91                                                                                        C                    92                                                                                        C                    93                                                                        )                    ⁢                      (                                                            B                  0                                ⁡                                  (                  n                  )                                            ⁢                                                          ⁢                                                B                  1                                ⁡                                  (                  n                  )                                            ⁢                                                          ⁢                                                B                  2                                ⁡                                  (                  n                  )                                            ⁢                                                          ⁢                                                B                  3                                ⁡                                  (                  n                  )                                                      )                                              (                  Eq          .                                          ⁢          1                )            
Eq. 1 can thus be rewritten as:I(n)=C B(n)  (Eq. 2)
Given a vector of intensities output by a CCD for each separation lane, the theory of determining the presence or absence of each of the M=4 bases from the R=10 wavelength channels is fairly well established. This is simply a particular case of an over-determined system in which a smaller number of unknowns is determined from a greater number of equations. After mathematical transformation, Eq. 2 can be written as:B(n)=(CTC)−1CTI(n)  (Eq. 3)where B0(n), . . . , B3(n) now represent the unknown values of the individual bases as functions of time index n, each value being reflective of the relative likelihood of the corresponding dye tagging that base being present; I0(n), I1(n), . . . I9(n) are the fluorescence intensities of the ten channels, and Cij's are the coefficients of wavelength i under known base j and where CT is a transpose of the matrix C and A=(CT C)−1 CT is the pseudo-inverse of matrix C. While in the above analysis, C is a 10×4 matrix because a total of ten channels and four bases are used, in the general case, C is an R×M matrix wherein R≧M, and R and M are both integers greater than 2.
Typically, in prior art systems, the calibration matrix C is determined at the time the system is created. More particularly, calibration matrix C is specific to a set of dyes that are used, and is constant for all separation lanes in a system. If such a prior art system is then modified, such as by upgrading to a new set of optical filters, the calibration matrix C needs to be re-calibrated.
FIG. 1 illustrates two shortcomings of using a constant calibration matrix for all capillaries in a capillary array. As seen in FIG. 1, the 0th order spectral intensities 102 from each of the capillaries do not map onto the same pixel in corresponding pixel columns. In particular, the 0th order spectral intensities from capillaries 7 and 10, which are detected in their corresponding pixel columns 104, 106, respectively, do not fall on the same-positioned pixel as do the 0th order spectral images from the remaining capillaries. Similarly, the 1st order spectral intensities 112 from capillaries 7 and 10 in these same columns also do not fall on the same-positioned pixels as do the 1st order spectral images from the remaining capillaries, but rather are offset by a skew of a single pixel. A consequence of this skewness, which may be caused by improper arrangement of capillaries 7 and 10 within the capillary array, is that the binning process for 1st order intensities from capillaries 7 and 10 results in a spectrum which would be slightly different than if the binning process started one pixel over. As a result, using a single calibration matrix C for all the capillaries, leads to imprecise results, when Eq. 3 is invoked to try to identify the due causes the detected fluorescence from capillaries 7 and 10. As also illustrated in FIG. 1, the 1st order spectral image 114 for capillary 1 maps onto one more pixel than do the spectral images of the remaining capillaries. This feature, which may be caused by such factors as coma, spherical aberrations, astigma, and lateral chromatic aberration of the grating image system, also may lead to imprecisions when binning followed by use of the calibration matrix as in Eq. 3.
In general, different dye sets have different spectra. As a consequence, each dye set has a different calibration matrix. Consequently, a further disadvantage of using a single calibration matrix for a multi-lane separation system, is that one cannot run multiple dye sets in different separation lanes.